{
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   "cell_type": "markdown",
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    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 逻辑回归预测考试成绩\n",
    "### 任务\n",
    "基于examdata.csv数据，建立逻辑回归模型，预Exam1 = 75，Exam2 = 60时，该同学在Exam3是passed or failed；建立二阶边界，提高模型准确度\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "       Exam1      Exam2  Pass\n0  34.623660  78.024693     0\n1  30.286711  43.894998     0\n2  35.847409  72.902198     0\n3  60.182599  86.308552     1\n4  79.032736  75.344376     1",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Exam1</th>\n      <th>Exam2</th>\n      <th>Pass</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>34.623660</td>\n      <td>78.024693</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>30.286711</td>\n      <td>43.894998</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>35.847409</td>\n      <td>72.902198</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>60.182599</td>\n      <td>86.308552</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>79.032736</td>\n      <td>75.344376</td>\n      <td>1</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 1
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "data = pd.read_csv('examdata.csv')\n",
    "data.head()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
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  {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# visualize the data\n",
    "from matplotlib import pyplot as plt\n",
    "fig1 = plt.figure()\n",
    "plt.scatter(data.loc[:, 'Exam1'], data.loc[:, 'Exam2'])\n",
    "plt.title('Exam1-Exam2')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "plt.show()\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "0     False\n1     False\n2     False\n3      True\n4      True\n      ...  \n95     True\n96     True\n97     True\n98     True\n99     True\nName: Pass, Length: 100, dtype: bool\n"
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# add label mask\n",
    "mask = data.loc[:, 'Pass'] == 1\n",
    "print(mask)\n",
    "fig2 = plt.figure()\n",
    "passed = plt.scatter(data.loc[:, 'Exam1'][mask], data.loc[:, 'Exam2'][mask])\n",
    "failed = plt.scatter(data.loc[:, 'Exam1'][~mask], data.loc[:, 'Exam2'][~mask])\n",
    "plt.title('Exam1-Exam2')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "plt.legend((passed, failed), ('passed', 'failed'))\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Exam1      Exam2\n0   34.623660  78.024693\n1   30.286711  43.894998\n2   35.847409  72.902198\n3   60.182599  86.308552\n4   79.032736  75.344376\n..        ...        ...\n95  83.489163  48.380286\n96  42.261701  87.103851\n97  99.315009  68.775409\n98  55.340018  64.931938\n99  74.775893  89.529813\n\n[100 rows x 2 columns]\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0    34.623660\n1    30.286711\n2    35.847409\n3    60.182599\n4    79.032736\nName: Exam1, dtype: float64"
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "source": [
    "# define X, y\n",
    "X = data.drop('Pass', axis=1)\n",
    "y = data.loc[:, 'Pass']\n",
    "X1 = data.loc[:, 'Exam1']\n",
    "X2 = data.loc[:, 'Exam2']\n",
    "print(X)\n",
    "X1.head()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "LogisticRegression()"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "# establish the model and train it\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "LR = LogisticRegression()\n",
    "LR.fit(X, y)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1\n 1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1\n 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1]\n0.89\n"
    }
   ],
   "source": [
    "# show the predicted result and its accuracy\n",
    "y_predict = LR.predict(X)\n",
    "print(y_predict)\n",
    "\n",
    "from sklearn.metrics import accuracy_score\n",
    "accuracy = accuracy_score(y, y_predict)\n",
    "print(accuracy)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[1]\n"
    }
   ],
   "source": [
    "# exam1 = 70, exam2 = 65\n",
    "y_test = LR.predict([[70, 65]])\n",
    "print(y_test)\n",
    "\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   }
  },
  {
   "cell_type": "code",
   "source": [
    "# 边界函数：θ₀ + θ₁X₁ + θ₂X₂ = 0\n",
    "theta0 = LR.intercept_\n",
    "theta1, theta2 = LR.coef_[0][0], LR.coef_[0, 1]\n",
    "print(theta0, theta1, theta2)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "execution_count": 8,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[-25.05219314] 0.20535491217790372 0.2005838039546903\n"
    }
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "0     89.449169\n1     93.889277\n2     88.196312\n3     63.282281\n4     43.983773\n        ...    \n95    39.421346\n96    81.629448\n97    23.219064\n98    68.240049\n99    48.341870\nName: Exam1, Length: 100, dtype: float64\n"
    }
   ],
   "source": [
    "# 决策边界\n",
    "X2_new = -(theta0 + theta1 * X1)/theta2\n",
    "print(X2_new)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "fig3 = plt.figure()\n",
    "passed = plt.scatter(data.loc[:, 'Exam1'][mask], data.loc[:, 'Exam2'][mask])\n",
    "failed = plt.scatter(data.loc[:, 'Exam1'][~mask], data.loc[:, 'Exam2'][~mask])\n",
    "plt.plot(X1, X2_new)\n",
    "plt.title('Exam1-Exam2')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "plt.legend((passed, failed), ('passed', 'failed'))\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "source": [
    "# 二阶边界函数：θ₀ + θ₁X₁ + θ₂X₂ + θ₃X₁² + θ₄X₂² + θ₅X₁X₂= 0\n",
    "# 假定X₁为已知\n",
    "# θ₄X₂² + (θ₅X₁ + θ₂)X₂ + (θ₀ + θ₁X₁ + θ₃X₁²) = 0\n",
    "# 根据二元一次方程求根公式：\n",
    "# ax^2+bx+c=0，x1=(-b+(b^2-4ac)^1/2)/2a,x2=(-b-(b^2-4ac)^1/2)/2a\n",
    "# 由于x2<0，所以只取x1\n",
    "# create new data\n",
    "X1_2 = X1 * X1\n",
    "X2_2 = X2 * X2\n",
    "X1_X2 = X1 * X2\n",
    "X_new = {'X1': X1, 'X2': X2, 'X1_2': X1_2, 'X2_2': X2_2, 'X1_X2': X1_X2}\n",
    "X_new = pd.DataFrame(X_new)\n",
    "print(X_new)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "execution_count": 11,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "X1         X2         X1_2         X2_2        X1_X2\n0   34.623660  78.024693  1198.797805  6087.852690  2701.500406\n1   30.286711  43.894998   917.284849  1926.770807  1329.435094\n2   35.847409  72.902198  1285.036716  5314.730478  2613.354893\n3   60.182599  86.308552  3621.945269  7449.166166  5194.273015\n4   79.032736  75.344376  6246.173368  5676.775061  5954.672216\n..        ...        ...          ...          ...          ...\n95  83.489163  48.380286  6970.440295  2340.652054  4039.229555\n96  42.261701  87.103851  1786.051355  7587.080849  3681.156888\n97  99.315009  68.775409  9863.470975  4730.056948  6830.430397\n98  55.340018  64.931938  3062.517544  4216.156574  3593.334590\n99  74.775893  89.529813  5591.434174  8015.587398  6694.671710\n\n[100 rows x 5 columns]\n"
    }
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "LogisticRegression()"
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "# establish new model and train it\n",
    "LR_2 = LogisticRegression()\n",
    "LR_2.fit(X_new, y)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "1.0\n"
    }
   ],
   "source": [
    "y2_predict = LR_2.predict(X_new)\n",
    "accuracy2 = accuracy_score(y, y2_predict)\n",
    "print(accuracy2)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# X1排序\n",
    "X1_new = X1.sort_values()\n",
    "theta0 = LR_2.intercept_\n",
    "theta1, theta2, theta3, theta4, theta5 = LR_2.coef_[0][0], LR_2.coef_[0][1], LR_2.coef_[0][2], LR_2.coef_[0][3], LR_2.coef_[0][4]\n",
    "a = theta4\n",
    "b = theta5 * X1_new + theta2\n",
    "c = theta0 + theta1 * X1_new + theta3 * X1_new * X1_new\n",
    "print(X_new)\n",
    "X2_new_boundary = (-b + np.sqrt(b * b - 4 * a * c))/(2 * a)\n",
    "print(X2_new_boundary)\n",
    "fig4 = plt.figure()\n",
    "plt.plot(X1_new, X2_new_boundary)\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "fig5 = plt.figure()\n",
    "passed = plt.scatter(data.loc[:, 'Exam1'][mask], data.loc[:, 'Exam2'][mask])\n",
    "failed = plt.scatter(data.loc[:, 'Exam1'][~mask], data.loc[:, 'Exam2'][~mask])\n",
    "plt.plot(X1_new, X2_new_boundary)\n",
    "plt.title('Exam1-Exam2')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "plt.legend((passed, failed), ('passed', 'failed'))\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  }
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